Cross-Diffusion Turing Instability — Chemotaxis

Cross-diffusion (e.g. chemotaxis: cells drift up a chemical gradient) can trigger Turing instability even when standard diffusion would not. Cells u aggregate toward attractant v, which cells consume. Patterns emerge from homogeneous initial conditions.

D_u (cell diff): 0.30 D_v (chem diff): 2.00 χ (chemotaxis): 1.50 Production r: 0.80 Decay d: 0.50

∂u/∂t = D_u∇²u − χ∇·(u∇v) + f(u,v) | ∂v/∂t = D_v∇²v + ru − dv | Keller-Segel chemotaxis